A384708 a(n) is the smallest integer k such that k is the sum of exactly n distinct permutations of k, all having the same number of digits as k.

1, 954, 4617, 5112, 8136, 67104, 76011, 90216, 910107

Offset: 1

Author

Gonzalo Martínez, Jun 07 2025

Keywords

• nonn
• base
• fini
• full

Comments

There is no such k exists for n >= 10, since the sum of 10 or more distinct permutations of any integer k, with the same number of digits of k, will always be greater than k itself.

Examples

			a(1) = 1, since 1 = 1.
a(2) = 954, since 954 = 459 + 495.
a(3) = 4617, since 4617 = 1467 + 1476 + 1674.
a(4) = 5112, since 5112 = 1125 + 1215 + 1251 + 1521.
a(5) = 8136, since 8136 = 1368 + 1386 + 1683 + 1836 + 1863.
a(6) = 67104, since 67104 = 10467 + 10476 + 10647 + 10674 + 10764 + 14076.
a(7) = 76011, since 76011 = 10167 + 10176 + 10617 + 10671 + 11067 + 11607 + 11706.
a(8) = 90216, since 90216 = 10269 + 10296 + 10629 + 10692 + 10962 + 12069 + 12609 + 12690.
a(9) = 910107, since 910107 = 100179 + 100197 + 100917 + 100971 + 101079 + 101097 + 101790 + 101907 + 101970. - _David A. Corneth_, Jun 12 2025
		

Crossrefs

Subsequence of A384433.

Cf. A055098.

Extensions

a(9) from David A. Corneth, Jun 12 2025